After a divorce the mother almost always gets to continue to live with her kids and maintain her role in there life. The father then becomes the geographically (and sometimes emotionally) distant parent.
This is a big challenge and one that is fundamental to moving on to be great dad for your kids despite the disruption of divorce.
The geographical problem can have a tremendous impact, travelling 30 miles or 300 miles has a major and very practical effect upon the amount of real contact a father can have with his children. Email and Social Media are OK but 22 year old computer geek has yet been able to write an algorithm that delivers a great big hug! There is nothing you can do about physical distance but everything you can do about emotional distance.
The great big thing to remember is that you are divorced from their mother not from them. Their need for you is now even greater. Don't let them down. Now is the opportunity to connect with them on your own terms and perhaps build an even better relationship than before.
Do your parenting your way but consider your ex wife's views on this
Your divorce set you free from your ex-wife's expectations but your parents, her parents and anybody else who has ever been a parent will have a view on how you are doing.
For the sake of the children it is good to have some continuity between how stuff works in his/her house and in yours. Having to spend time in two completely different domestic environments will be very hard for them and require their constant adjustment as they move from one to another.
Act naturally, be yourself and help them feel relaxed
There's no need to keep buying presents or keep them perpetually entertained. They will be just as happy to be with you as you are to be with them, do stuff together but also spend time chilling out.
Your children now have two homes and they are not the same
Your kids have one home with mum and another with dad. They don't visit you, they live with you and they will need to understand there will be differences between their two homes. "But Mom lets us" does not mean that automatically you will too.
You are not a part time dad, you are full time dad who is not always there
Being a dad is not something you can be slightly. It's like being pregnant, you either are or you aren't. Many divorced dads get to spend more quality time with their kids than fathers in complete families. No matter how much time you spend with your children, if you are totally committed and see them regularly and responsibly, you're a dad and as good as any other dad in the world.
Kids can be more resilient than you think
Divorce doesn't necessarily mean that it's time for everyone to have therapy to help cope with life after divorce. But they will need help to understand that your love and your ex-wife's come undiminished and unaffected by the fact that their parents no longer love each other.
Stuff will go wrong and that's not the end of the world
You are going to make mistakes, you are not perfect but then nobody else is either. Making mistakes is a fundamental part of parenting. We all do it and like all mistakes it is vital to learn from them. Stick to your principles of how you want your children to be brought up and if you deliver your daughter to a birthday party with her T-shirt on back to front then there is likely to be no lasting psychological damage from the experience.